Formula For a plus b whole square (a + b)2 = a2 + 2ab + b2

Formula For a plus b whole square

(a + b)2 = a2 + 2ab + b2
Question 1 :
Expand (5x + 3)²
Solution:
Here the given question is in the form of (a+b)². Instead of a we have "5x" and instead of b we have "3" .
So we need to apply the formula a² + 2ab + b² and we need to apply those values of a and b
a = 5 x and b = 3

(5x + 3)² = (5x)² + 2 (5x) (3) + (3)²

          = 25x² + 30 x + 9

          = 25x² + 30 x + 9             

Question 2 :
Expand (x + 2) ²
Solution:
Here the question is in the form of (a+b) ². Instead of a we have "x" and instead of b we have "2".
So we need to apply the formula a² + 2ab + b ² and we need to apply those values of a and b
a = x   and b = 2

(x + 2)² = (x)² + 2 (x) (2) + (2)²

          = x² + 4 x + 4

Question 3 :
If a + b = 3 and a² + b² = 29,find the value of ab.
Solution:
In this problem to get the value of ab we can use the formula for a plus b whole square that is  (a + b)² = a² + b² - 2 a b
3² = 29 - 2ab
9 = 29 - 2 ab
2 a b = 29 - 9
2 a b = 20
ab = 20/2
ab = 10

Question 4 :
[√2 + (1/√ 2)]²  is equal to
Solution:
(a + b)² = a² + b² + 2 a b
a = √2  b = 1/√2
[√2 + (1/√ 2)]² = ( √2 )² + (1/√2)² + 2 √2 (1/√2)
                     = 2 + (1/2) + 2
                     = 4 + (1/2)
                     = 9/2

Question 5 :
(105)²  is equal to
Solution:
Instead of multiplying 105 x 105 to get the value of (105)² we can use algebraic formula for a plus b whole square that is  (a+b)² to get the same answer.105 can be written as 100 + 5.
(105)² = (100 + 5)²
(a + b)² = a² + b² + 2 a b
a = 100  b = 5
(105)² = (100)² + (5)² + 2 (100)(5)
         = 10000 + 25 + 1000
         = 11025

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